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ON  THE MOTION  OF PENDULUMS.
97
and remarks with justice that no sensible error would thence result in the length of the seconds' pendulum, as determined by his method, but that the factor k would belong to the system of the two pendulums.
The following is the result of the comparison of theory and experiment in the case of Bessel's experiments on the oscillations of spheres in air.
Value of k belonging to the system of a long and a short pendulum, as determined experimentally by Bessel....................................... 0*956
Value deduced from theory, including the correction for the wire, but not the correction for confined space .. .................................... 0*817
difference    + 0*139
I cannot find that Bessel has stated exactly the distance of the centre of the sphere from the back of the frame within which it was swung, but if we may judge by the sketch of the whole apparatus which is given in Plate I., and by a comparison of figs. 2 and 3, Plate II., it must have been very small, that is to say, a small fraction of the radius of the sphere *. If so, although the exact calculation of the correction for confined space would form a problem of extreme difficulty, it may be shewn from theoretical considerations that the correction would be by no means insensible, so that it might wholly or in part account for the difference 4- 0*139 between the results of theory and observation. It is, however, not improbable, for a reason which has been already mentioned, that the theoretical correction for the wire is not quite exact.
64 The experiments performed by Bessel on a sphere vibrating in water will be more conveniently considered after the discussion of some experiment of Coulomb's, to which I now proceed. These experiments are contained in a memoir entitled
* The measurement of either of Bessel's figures, figs. 5 or 6, Plate II. gives 1-53 inch for the distance of the centre of the sphere from the surface of the broad iron bar which formed the back of the frame, the surface of the bar being supposed truly vertical; and the measurement of fig. 2 giving 2-06 inches for the diameter of the sphere, it appears that the distance of the surface of the sphere from the surface of the bar was barely equal to half the radius of the sphere.
S. IIT.                                                                                                   7
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